MIMO Fading Channel
Filter input signal through MIMO multipath fading channel
 Library:
Communications Toolbox / Channels
Communications Toolbox / MIMO
Description
The MIMO Fading Channel block filters an input signal using a multiinput/multioutput (MIMO) multipath fading channel. This block models both Rayleigh and Rician fading and employs the Kronecker model for modeling the spatial correlation between the links. For processing details, see the Algorithms section.
Signal Dimensions
The availability and dimensions of input and output port signals depends on:
The Antenna selection parameter setting on the Main tab
The Initial time source parameter setting on the Realization tab
The Output channel path gains selection on the Realization tab
Antenna Selection Parameter  Signal Input (in)  Transmit Selection Input (Tx Sel)  Receive Selection Input (Rx Sel)  Initial Time Offset Input (Init Time)  Signal Output (Out1)  Optional Channel Gain Output (Gain) 

Off  N_{S}byN_{T}  N/A  N/A  nonnegative scalar  N_{S}byN_{R}  N_{S}byN_{P}byN_{T}byN_{R} 
Tx  N_{S}byN_{ST}  1byN_{T}  N/A  N_{S}byN_{R}  
Rx  N_{S}byN_{T}  N/A  1byN_{R}  N_{S}byN_{SR}  
Tx and Rx  N_{S}byN_{ST}  1byN_{T}  1byN_{R}  N_{S}byN_{SR} 
N_{S} represents the number of samples in the input signal.
N_{T} represents the number of transmit antennas, as determined by:
Transmit spatial correlation when Specify spatial correlation is set to
Separate Tx Rx
Number of transmit antennas when Specify spatial correlation is set to
None
orCombined
N_{R} represents the number of receive antennas, as determined by:
Receive spatial correlation when Specify spatial correlation is set to
Separate Tx Rx
Number of receive antennas when Specify spatial correlation is set to
None
Combined spatial correlation and Number of transmit antennas when Specify spatial correlation is set to
Combined
N_{P} represents the number of channel paths, as determined by the Discrete path delays (s) or Average path gains (dB).
N_{ST} represents the number of selected transmit antennas, as determined by the number of elements set to
1
in the vector provided to the Tx Sel input port.N_{SR} represents the number of selected receive antennas, as determined by the number of elements set to
1
in the vector provided to the Rx Sel input port.
Ports
Input
in
— Input data signal
vector
Input data signal, specified as an N_{S}byN_{T} or N_{S}byN_{ST} matrix.
N_{S} represents the number of samples in the input signal.
N_{T} represents the number of transmit antennas.
N_{ST} represents the number of selected transmit antennas.
Data Types: double
 single
Complex Number Support: Yes
Tx Sel
— Select active transmit antennas
binary vector
Select active transmit antennas, specified as a
1byN_{T} binary vector.
N_{T} represents the number of transmit antennas.
Elements set to 1
identify selected antenna indices and
0
identify nonselected antenna indices.
Dependencies
To enable this port, on the Main tab, set Antenna selection
to Tx
or Tx and Rx
.
Data Types: double
Rx Sel
— Select active receive antennas
binary vector
Select active receive antennas, specified as a
1byN_{R} binary vector.
N_{R} represents the number of receive antennas.
Elements set to 1
identify selected antenna indices and
0
identify nonselected antenna indices.
Dependencies
To enable this port, on the Main tab, set Antenna selection
to Rx
or Tx and Rx
.
Data Types: double
Init Time
— Initial time offset
nonnegative scalar
Initial time offset for the fading model in seconds, specified as a nonnegative scalar.
Init Time must be greater than the last frame end time. When
Init Time is not a multiple of 1/Sample rate (Hz)
, it is rounded up to the nearest sample position.
Dependencies
To enable this port, on the Realization tab, set Initial time source to Input port
.
Data Types: double
Output
Out1
— Output data signal for fading channel
vector
Output data signal for the fading channel, returned as an N_{S}byN_{R} or N_{S}byN_{SR} matrix.
N_{S} represents the number of samples in the input signal.
N_{R} represents the number of receive antennas.
N_{SR} represents the number of selected receive antennas.
Gain
— Discrete path gains
4D array
Discrete path gains of the underlying fading process, returned as an N_{S}byN_{P}byN_{T}byN_{R} array.
N_{S} represents the number of samples in the input signal.
N_{P} represents the number of channel paths.
N_{T} represents the number of transmit antennas.
N_{R} represents the number of receive antennas.
Entries for nonselected paths are filled with NaN
.
Dependencies
To enable this port, on the Realization tab, select Output channel path gains.
Parameters
Main Tab
Multipath parameters (frequency selectivity)Inherit sample rate from input
— Option to inherit the sample rate from input
on (default)  off
Select this parameter to use the sample rate of the input signal when processing. When
Inherit sample rate from input
is selected, the sample rate is
N_{S}/T_{S},
where N_{S} is the number of input samples, and
T_{S} is the model sample time.
Sample rate (Hz)
— Input signal sample rate
1
(default)  positive scalar
Input signal sample rate, specified in hertz as a positive scalar. To match the model settings, set the sample rate to N_{S}/T_{S}, where N_{S} is the number of input samples, and T_{S} is the model sample time.
Dependencies
This parameter appears when Inherit sample rate from input is not selected.
Data Types: double
Discrete path delays (s)
— Delays for each discrete path
0
(default)  nonnegative scalar  row vector
Delays for each discrete path in seconds, specified as a nonnegative scalar or row vector.
When you set Discrete path delays (s) to a scalar, the MIMO channel is frequency flat.
When you set Discrete path delays (s) to a vector, the MIMO channel is frequency selective.
Data Types: double
Average path gains (dB)
— Average gain for each discrete path
0
(default)  scalar  row vector
Average gain for each discrete path in decibels, specified as a scalar or row vector. Average path gains (dB) must have the same size as Discrete path delays (s).
Data Types: double
Normalize average path gains to 0 dB
— Option to normalize average path gains to 0 dB
on (default)  off
Select this parameter to normalize the fading processes so that the total power of the path gains, averaged over time, is 0 dB.
Fading distribution
— Fading distribution of channel
Rayleigh
(default)  Rician
Select the fading distribution of the channel, either
Rayleigh
or Rician
.
Kfactors
— Kfactor of Rician fading channel
3
(default)  positive scalar  row vector of nonnegative values
Kfactor of a Rician fading channel, specified as a positive scalar or a 1byN_{P} vector of nonnegative values. N_{P} equals the value of the Discrete path delays (s) parameter.
If you set Kfactors to a scalar, the first discrete path is a Rician fading process with a Rician Kfactor of Kfactors. Any remaining discrete paths are independent Rayleigh fading processes.
If you set Kfactors to a row vector, the discrete path corresponding to a positive element of the Kfactors vector is a Rician fading process with a Rician Kfactor specified by that element. The discrete path corresponding to any zerovalued elements of the Kfactors vector are Rayleigh fading processes. At least one element value must be nonzero.
Dependencies
This parameter appears when Fading distribution is Rician
.
Data Types: double
LOS path Doppler shifts (Hz)
— Doppler shifts for lineofsight components
0
(default)  scalar  row vector
Doppler shifts for the lineofsight components of the Rician fading channel in hertz, specified as a scalar or row vector. This parameter must have the same size as Kfactors.
If you set LOS path Doppler shifts (Hz) to a scalar, it represents the lineofsight component Doppler shift of the first discrete path that is a Rician fading process.
If you set LOS path Doppler shifts (Hz) to a row vector, the discrete path that is a Rician fading process has its lineofsight component Doppler shift specified by the elements of LOS path Doppler shifts (Hz) that correspond to positive elements in the Kfactors vector.
Dependencies
This parameter appears when Fading distribution is Rician
.
Data Types: double
LOS path initial phases (rad)
— Initial phases for lineofsight components
0
(default)  scalar  row vector
Initial phases for the lineofsight component of the Rician fading channel in radians, specified as a scalar or row vector. This parameter must have the same size as Kfactors.
If you set LOS path initial phases (rad) to a scalar, it is the lineofsight component initial phase of the first discrete path that is a Rician fading process.
If you set LOS path initial phases (rad) to a row vector, the discrete path that is a Rician fading process has its lineofsight component initial phase specified by the elements of LOS path initial phases (rad) that correspond to positive elements in the Kfactors vector.
Dependencies
This parameter appears when Fading distribution is Rician
.
Data Types: double
Maximum Doppler shift (Hz)
— Maximum Doppler shift for all channel paths
0.001
(default)  nonnegative scalar
Maximum Doppler shift for all channel paths in hertz, specified as a nonnegative scalar.
Maximum Doppler shift (Hz) must be smaller than (Sample rate (Hz)/10)/f_{c} for each path, where f_{c} is the cutoff frequency factor of the path. For more information, see Cutoff Frequency Factor.
Data Types: double
Doppler spectrum
— Doppler spectrum shape for all channel paths
doppler('Jakes')
(default)  doppler('Flat')
 doppler('Rounded', ...)
 doppler('Bell', ...)
 doppler('Asymmetric Jakes', ...)
 doppler('Restricted Jakes', ...)
 doppler('Gaussian', ...)
 doppler('BiGaussian', ...)
Doppler spectrum shape for all channel paths, specified as a single Doppler spectrum
structure returned from the doppler
function or a
1byN_{P} cell array of such structures. The default
value of this parameter is the Jakes Doppler spectrum (doppler('Jakes')
).
If you assign a single call to
doppler
, all paths have the same specified Doppler spectrum.If you assign a 1byN_{P} cell array of calls to
doppler
using any of the specified syntaxes, each path has the Doppler spectrum specified by the corresponding Doppler spectrum structure in the array. In this case, N_{P} equals the value of the Discrete path delays (s) parameter.
Dependencies
This parameter applies when Maximum Doppler shift (Hz) is greater than zero.
If the Technique for generating fading samples parameter is set to Sum of sinusoids
,
Doppler spectrum
must be doppler('Jakes')
.
Specify spatial correlation
— Spatial correlation mode
None
(default)  Separate Tx Rx
 Combined
Select the spatial correlation mode: None
,
Separate Tx Rx
, or Combined
.
Choose
'None'
to specify the number of transmit and receive antennas.Choose
'Spatial Tx Rx'
to specify the transmit and receive spatial correlation matrices separately. The number of transmit (N_{T}) and receive (N_{R}) antennas are derived from the dimensions of the Transmit spatial correlation and Receive spatial correlation parameters, respectively.Choose
'Combined'
to specify a single correlation matrix for the whole channel. The product of N_{T} and N_{R} is derived from the dimension of Combined spatial correlation.
Number of transmit antennas
— Number of transmit antennas
2
(default)  positive integer
Number of transmit antennas, specified as a positive integer.
Dependencies
This parameter appears when Specify spatial correlation is None
or Combined
.
Data Types: double
Number of receive antennas
— Number of receive antennas
2
(default)  positive integer
Number of receive antennas, specified as a positive integer.
Dependencies
This parameter appears when Specify spatial correlation is None
.
Data Types: double
Transmit spatial correlation
— Spatial correlation of transmitter
[1 0; 0 1]
(default)  matrix  3D array
Specify the spatial correlation of the transmitter as an N_{T}byN_{T} matrix or N_{T}byN_{T}byN_{P} array. N_{T} is the number of transmit antennas, and N_{P} equals the value of the Discrete path delays (s) parameter.
If Discrete path delays (s) is a scalar, the channel is frequency flat, and Transmit spatial correlation is an N_{T}byN_{T} Hermitian matrix. The magnitude of any offdiagonal element must be no larger than the geometric mean of the two corresponding diagonal elements.
If Discrete path delays (s) is a vector, the channel is frequency selective, and you can specify Transmit spatial correlation as a matrix. Each path has the same transmit spatial correlation matrix.
Alternatively, you can specify Transmit spatial correlation as an N_{T}byN_{T}byN_{P} array, where each path can have its own different transmit spatial correlation matrix.
Dependencies
This parameter appears when Specify spatial correlation is Separate Tx Rx
.
Data Types: double
Complex Number Support: Yes
Receive spatial correlation
— Spatial correlation of receiver
[1 0; 0 1]
(default)  matrix  3D array
Specify the spatial correlation of the receiver as an N_{R}byN_{R} matrix or N_{R}byN_{R}byN_{P} array. N_{R} is the number of receive antennas, and N_{P} equals the value of the Discrete path delays (s) parameter.
If Discrete path delays (s) is a scalar, the channel is frequency flat, and Receive spatial correlation is an N_{R}byN_{R} Hermitian matrix. The magnitude of any offdiagonal element must be no larger than the geometric mean of the two corresponding diagonal elements.
If Discrete path delays (s) is a vector, the channel is frequency selective, and you can specify Receive spatial correlation as a matrix. Each path has the same receive spatial correlation matrix.
Alternatively, you can specify Receive spatial correlation as an N_{R}byN_{R}byN_{P} array, where each path can have its own different receive spatial correlation matrix.
Dependencies
This parameter appears when Specify spatial correlation is Separate Tx Rx
.
Data Types: double
Complex Number Support: Yes
Combined spatial correlation
— Combined spatial correlation matrix
[1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1]
(default)  matrix  3D array
Specify the combined spatial correlation matrix as an N_{TR}byN_{TR} matrix or N_{TR}byN_{TR}byN_{P} array, where N_{TR} = (N_{T} ✕ N_{R}), and N_{P} equals the number of delay paths specified by the Discrete path delays (s) parameter.
If Discrete path delays (s) is a scalar, the channel is frequency flat, and Combined spatial correlation is an N_{TR}byN_{TR} Hermitian matrix. The magnitude of any offdiagonal element must be no larger than the geometric mean of the two corresponding diagonal elements.
If Discrete path delays (s) is a vector, the channel is frequency selective, and you can specify Combined spatial correlation as a matrix. Each path has the same spatial correlation matrix.
Alternatively, you can specify Combined spatial correlation as an N_{TR}byN_{TR}byN_{P} array, where each path can have its own different combined spatial correlation matrix.
Dependencies
This parameter appears when Specify spatial correlation is Combined
.
Data Types: double
Complex Number Support: Yes
Normalize outputs by number of receive antennas
— Normalize channel output
on (default)  off
Select this parameter to normalize the channel outputs by the number of receive antennas.
Simulate using
— Compilation type
Interpreted execution
(default)  Code generation
Compilation type, specified as Interpreted execution
or
Code generation
.
Antenna selection
— Antenna mode
Off
(default)  Tx
 Rx
 Tx and Rx
The antenna mode you select corresponds to additional input ports on the block.
Antenna selection Setting  Input Ports Added 

Off  None 
Tx  Tx Sel 
Rx  Rx Sel 
Tx and Rx  Tx Sel, Rx Sel 
Realization Tab
Technique for generating fading samples
— Channel modeling technique
Filtered Gaussian noise
(default)  Sum of sinusoids
Select the channel modeling technique, either Filtered Gaussian
noise
or Sum of sinusoids
.
Number of sinusoids
— Number of sinusoids used
48
(default)  positive integer
Number of sinusoids used to model the fading process, specified as a positive integer.
Dependencies
This parameter appears when Technique for generating fading samples is Sum of sinusoids
.
Initial time source
— Source of initial time offset
Property
(default)  Input port
Indicate the source of the initial time offset for the fading model, either
Property
or Input port
.
When you set Initial time source to
Property
, use Initial time (s) to set the initial time offset.When you set Initial time source to
Input port
, use the input port Init Time to set the initial time offset.
Dependencies
This parameter appears when Technique for generating fading samples is Sum of sinusoids
.
Initial time (s)
— Initial time offset
0
(default)  nonnegative scalar
Initial time offset for the fading model, specified as a nonnegative scalar.
When Initial time (s)
is not a multiple of
1/
Sample rate (Hz),
it is rounded up to the nearest sample position.
Dependencies
This parameter appears when Technique for generating fading samples is Sum of sinusoids
and Initial time source is set to Property
.
Initial seed
— Random number generator initial seed
73
(default)  nonnegative integer
Random number generator initial seed for this block, specified as a nonnegative integer.
Output channel path gains
— Option to output channel path gains
off (default)  on
Select this parameter to add the Gain output port to the block and output the channel path gains of the underlying fading process.
Visualization Tab
Channel visualization
— Select the channel visualization
Off
(default)  Impulse response
 Frequency response
 Doppler spectrum
 Impulse and frequency responses
Select the channel visualization: Off
, Impulse
response
, Frequency response
, Doppler
spectrum
, or Impulse and frequency responses
. When
visualization is on, the selected channel characteristics, such as impulse response or
Doppler spectrum, display in a separate window. For more information, see Channel
Visualization.
Dependencies
To enable this parameter set the Technique for generating
fading samples
parameter to Filtered Gaussian
noise
.
Antenna pair to display
— Transmitreceive antenna pair to display
[1,1]
(default)  vector
Transmitreceive antenna pair to display, specified as a 1by2 vector, where the first element corresponds to the desired transmit antenna and the second corresponds to the desired receive antenna. At this time, only a single pair can be displayed.
Dependencies
This parameter appears when Channel
visualization
is not Off
.
Percentage of samples to display
— Percentage of samples to display
25%
(default)  10%
 50%
 100%
Select the percentage of samples to display: 10%
,
25%
, 50%
, or
100%
. Increasing the percentage improves display accuracy at the
expense of simulation speed.
Dependencies
This parameter appears when Channel visualization is Impulse response
,
Frequency response
, or Impulse and frequency
responses
.
Path for Doppler spectrum display
— Path for which Doppler spectrum is displayed
1
(default)  positive integer
Path for which the Doppler spectrum is displayed, specified as a positive integer from 1 to N_{P}, where N_{P} equals the value of the Discrete path delays (s) parameter.
Dependencies
This parameter appears when Channel visualization is Doppler spectrum
.
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

Algorithms
The fading processing per link is described in Methodology for Simulating Multipath Fading Channels and assumes the same parameters for all (N_{T} × N_{R}) links of the MIMO channel. Each link comprises all multipaths for that link.
The Kronecker Model
The Kronecker model assumes that the spatial correlations at the transmit and receive sides are separable. Equivalently, the direction of departure (DoD) and directions of arrival (DoA) spectra are assumed to be separable. The full correlation matrix is:
$${R}_{H}=E\left[{R}_{t}\otimes {R}_{r}\right]$$
The ⊗ symbol represents the Kronecker product.
R_{t} is the correlation matrix at the transmit side, $${R}_{t}=E\left[{H}^{H}H\right]$$, and is of size N_{T}byN_{T}.
R_{r} is the correlation matrix at the receive side, $${R}_{r}=E\left[H{H}^{H}\right]$$, and is of size N_{R}byN_{R}.
You can obtain a realization of the MIMO channel matrix as:
$$H={R}_{r}^{\frac{1}{2}}A{R}_{t}^{\frac{1}{2}}$$
A is an N_{R}byN_{T} matrix of independent identically distributed complex Gaussian variables with zero mean and unit variance.
Cutoff Frequency Factor
The cutoff frequency factor, f_{c}, is dependent on the type of Doppler spectrum.
For any Doppler spectrum type other than Gaussian and biGaussian, f_{c} equals 1.
For a
doppler
('Gaussian')
spectrum type, f_{c} equalsNormalizedStandardDeviation
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.For a
doppler
('BiGaussian')
spectrum type:If the
PowerGains
(1)
andNormalizedCenterFrequencies
(2)
field values are both0
, then f_{c} equalsNormalizedStandardDeviation
(1)
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.If the
PowerGains
(2)
andNormalizedCenterFrequencies
(1)
field values are both0
, then f_{c} equalsNormalizedStandardDeviation
(2)
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.If the
NormalizedCenterFrequencies
field value is[0,0]
and theNormalizedStandardDeviation
field has two identical elements, then f_{c} equalsNormalizedStandardDeviation
(1)
$$\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\sqrt{2\mathrm{log}2}$$.In all other cases, f_{c} equals 1.
Antenna Selection
When the object is in antennaselection mode, it uses these algorithms to process an input signal.
All random path gains are always generated and keep evolving for each link, whether or not a given link is selected. The path gain values output for the nonselected links are populated with
NaN
.The spatial correlation applies to only the selected transmit and receive antennas, and the correlation coefficients are the corresponding entries in the transmit, receive, or combined correlation matrices. That is, the spatial correlation matrix for the selected transmit or receive antennas is a submatrix of the transmit, receive, or combined spatial correlation matrix property value.
For signal paths that are associated with nonactive antennas, a signal with zero power is transmitted to the channel filter.
Channel output normalization happens over the number of selected receive antennas.
References
[1] Oestges, C., and B. Clerckx. MIMO Wireless Communications: From RealWorld Propagation to SpaceTime Code Design. Academic Press, 2007.
[2] Correira, L. M. Mobile Broadband Multimedia Networks: Techniques, Models and Tools for 4G. Academic Press, 2006.
[3] Kermoal, J. P., L. Schumacher, K. I. Pedersen, P. E. Mogensen, and F. Frederiksen. "A stochastic MIMO radio channel model with experimental validation." IEEE Journal on Selected Areas of Communications. Vol. 20, Number 6, 2002, pp. 1211–1226.
[4] Jeruchim, M., P. Balaban, and K. S. Shanmugan. Simulation of Communication Systems. Second Edition. New York: Kluwer Academic/Plenum, 2000.
[5] Pätzold, Matthias, ChengXiang Wang, and Bjorn Olav Hogstand. "Two New SumofSinusoidsBased Methods for the Efficient Generation of Multiple Uncorrelated Rayleigh Fading Waveforms." IEEE Transactions on Wireless Communications. Vol. 8, Number 6, 2009, pp. 3122–3131.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
See Also
Blocks
Functions
Objects
Topics
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